PVRB plays an important role in network consensus organization. Transactions in blockchains are protected by the sender's signature, and the only way to "attack a transaction" is to include or exclude it from the block (or several blocks) in different moments of time. So, the main function of the consensus algorithm is establishing the order of transactions and blocks including them. Also, an essential feature of blockchains in reality is finality - the ability of a network to agree that the chain up to the finalized block is final and will never be excluded in case of a new fork. Usually, in order to agree that a block is valid and, most importantly, final, it is required to collect signatures from most block producers (hereinafter referred to as BPs) that at least involves delivering a chain of blocks to all BPs and distributing signatures between all BPs.
As the number of BPs grows, the volume of required network messages grows exponentially; therefore, consensus algorithms requiring finality, such as those used in Hyperledger, already do not work in case of several dozen BPs, since a huge number of interactions is required.
If the network has an undeniable and fair PVRB, then you can select one of BPs and appoint him a "leader" for one protocol round. If we have an N number of BPs where M: M > 1/2 N are honest: they do not censor transactions and do not build chain forks to perform a "double spend" attack, then using a uniformly distributed undeniable PVRB will allow you to choose a honest leader with probability rate equal to M / N (M / N> 1/2). If each leader is assigned a time slot during which he can produce a block and validate a chain, and with these slots being equal, the block chain of honest BPs will be longer than the chain formed by malicious BPs, and the consensus algorithm relying on the chain length will simply discard the "bad" one. This principle of allocating equal time slots to each BP was first used in Graphene (EOS predecessor) and allows to approve most blocks with a single signature, that greatly reduces the network load and ensures high consensus speed and stability. However, in EOS, it is necessary to use special blocks (Last Irreversible Block), which are confirmed by 2/3 + 1 of BP signatures. These blocks serve to ensure finality (the impossibility of a chain fork that begins prior to the last Last Irreversible Block).
Also, in real use cases the protocol scheme is more complex - voting for the proposed blocks involves several stages in order to support the network in case of missing blocks and network issues; but even with this in mind, consensus algorithms using PVRB require significantly fewer messages between BPs allowing to make them faster than the traditional PBFT or its various modifications.
The most prominent example of such algorithms is: Ouroboros
by Cardano team, that was announced to have mathematically provable resistance to BP collusion.
In Ouroboros, PVRB is used to define the so-called "BP schedule", according to which each BP is assigned a time slot for block publishing. The big advantage of PVRB is a complete BP "equality" (according to their balance sizes). PVRB fairness guarantees that malicious BPs cannot control the schedule of time slots, and therefore cannot manipulate the chain, preparing and analyzing chain forks in advance. To choose a fork it is enough to rely on the chain length without tricky calculations of BP "utility" or "weight" of its blocks.
In general, in case you need to select a random participant in a decentralized network, PVRB is usually better than, for instance, a deterministic variant based on a block hash. Without PVRB, the ability to influence the participant's choice leads to attacks, when out of several available options, the attacker chooses the next corrupt participant or some of them at once to ensure a more significant stake in the decision making. PVRB discredits these types of attacks.